Pound chicken breasts to an even 1/2-inch thickness using a meat mallet.
In a small bowl, combine salt, pepper, garlic powder, and onion powder; season both sides of the chicken.
Heat olive oil in a large heavy-bottomed skillet or grill pan over medium-high heat.
Cook chicken for 6-8 minutes per side until the internal temperature reaches 165°F (74°C); remove from skillet and tent with foil to keep warm.
In the same skillet, melt butter over medium heat. Add sliced onions and mushrooms.
Sauté vegetables for 5-7 minutes until the mushrooms are browned and onions are soft and translucent.
Arrange the cooked chicken breasts back in the skillet or on a baking sheet.
Top each chicken breast with an equal portion of the sautéed mushrooms and onions.
Place one slice of Monterey Jack cheese over the vegetable topping on each breast.
Cover the skillet with a lid for 2 minutes, or place under a broiler for 1-2 minutes, until the cheese is completely melted and bubbly.
Serve immediately, topped with warm cream gravy if desired.